Avery is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Avery will earn $40 every time one of her songs is played in a commercial and she will earn $140 every time one of her songs is played in a movie. Avery earned a total of $480 in royalties on 7 commercials and movies. Determine the number of commercials and the number of movies on which Avery's songs were played.

Let's denote the number of commercials as $C$ and the number of movies as $M$.

We know the following:

1. Avery earns $40 per commercial.
2. Avery earns $140 per movie.
3. The total earnings are $480.
4. The total number of commercials and movies is 7.

We can set up the following system of equations based on the information given:

1. $40C + 140M = 480$
2. $C + M = 7$

First, solve the second equation for $C$:

$C = 7 - M$

Next, substitute $C = 7 - M$ into the first equation:

$40(7 - M) + 140M = 480$

Distribute the 40:

$280 - 40M + 140M = 480$

Combine like terms:

$280 + 100M = 480$

Subtract 280 from both sides:

$100M = 200$

Divide by 100:

$M = 2$

Now, substitute $M = 2$ back into the second equation to find $C$:

$C + 2 = 7$

Subtract 2 from both sides:

$C = 5$

So, the number of commercials is 5 and the number of movies is 2.

Let's denote the number of commercials as $C$ and the number of movies as $M$.

We know the following:

1. Avery earns $40 for each commercial.
2. Avery earns $140 for each movie.
3. The total earnings are $480.
4. The total number of commercials and movies is 7.

We can set up the following system of equations based on the information given:

1. $40C + 140M = 480$ (total earnings equation)
2. $C + M = 7$ (total number of commercials and movies)

First, solve the second equation for $C$:

$C = 7 - M$

Next, substitute $C = 7 - M$ into the first equation:

$40(7 - M) + 140M = 480$

Distribute the 40:

$280 - 40M + 140M = 480$

Combine like terms:

$280 + 100M = 480$

Subtract 280 from both sides:

$100M = 200$

Divide by 100:

$M = 2$

Now, substitute $M = 2$ back into the equation $C = 7 - M$:

$C = 7 - 2$

$C = 5$

So, Avery's songs were played in 5 commercials and 2 movies.